Before my brief break, I was writing a series on a
recent article by Sean
Carroll. This is taking me several posts to respond to it fully, so I am going one section at
a time.
My first post
gave an introduction to the topic, and covered Carroll's own introduction.
My second post
discussed his first main section, where he established his definitions
and described the scope of his discussion.
Now we ask what do we mean by "Something" and "Nothing."

This is a topic of some importance. The main criticism levied against
physicists who attempt to address this topic is that they don't start with
Nothing as the philosophers understand it. They might start with a quantum
vacuum, or gravity, and say that the universe can arise from those.
That obviously doesn't answer the question, but merely pushes it back.
We have to ask what explains the quantum vacuum, or gravity. Indeed, it
is impossible for the physicist use physics to get to Something from
Nothing. Why? Because the physicist assumes that there are various laws
and regularities governing the material universe. He has two goals:
1) to discover what those laws are, and 2) to uncover the consequences of
those laws. So a physicist might well say, "Given these laws of physics,
a universe such as the one we live in is bound to emerge," but he cannot
go much further than that. Perhaps the physicist can reduce the laws of
physics to some deeper principle, such as symmetry, but that is still not
to explain why those symmetries hold and not some others. We are able to
construct numerous consistent physical theories based on different
symmetries. So why would these symmetries given the universe and not
others? It is at this point that the physicist needs to hand over to the
philosophers (whether professional, amateur, or even the physicist
himself squatting in somebody else's department).

To his credit, Professor Carroll understands this point. He distinguishes
the question into two parts. Firstly, why there is stuff (matter, energy
and so on), and secondly why there is anything at all. Answers are often
made to answer the first question, but these have little relevance to the
second question. Yet it is this second question that people want to be
answered.

Carroll continues to discuss the various progressions in physics. Newton
imagined an absolute space and absolute time that passed indefinitely into
the past. Special and general relativity combine space and time into
demanding a universe which began with a singularity (could that represent
the transaction from something to nothing?)

But quantum mechanics is the big change. For one thing, the philosophy
of quantum mechanics is unclear. One thing that all agree on is
the centrality of the wavefunction. But what is this? Carroll lists the
Everett multiple worlds formulation as an example of a theory where the
wavefunction is everything. There are also approaches
such as the De-Broglie/Bohm approach where there are additional degrees
of freedom in addition to the wavefunction. Carroll will focus on the
wavefunction as describing everything approach.

Certainly he has some justification for this; De-Broglie/Bohm famously
struggles with relativity. But this is the first point where I might
question Carroll's approach. There are many interpretations besides the
two that he mentions; by focussing
only on one of them risks missing something important if that
interpretation turns out to be incorrect. After all, the Everett
interpretation with its branching universes is wholly unintuitive, and
still begs the question of why the universe would behave in that way.

But of course (and this is the point that I keep making), we need to
move beyond quantum mechanics. Quantum mechanics is a compromise between
the philosophy of classical mechanics and the philosophy of quantum
field theory (which I believe to be Aristotelian).
Quantum mechanics itself is not Aristotelian, because some of its
premises are taken from mechanism. Among these is the idea that there is
a fixed number of particles. In field theory, we no longer think that way.

Carroll indeed abandons the particle interpretation entirely. The focus
of field theory, he writes, is on fields which permeate all space, rather
than positions of individual particles. This statement has, I think, the
merit of being partially true and partially false. Even though we see
fields spreading through all space, the focus is on individual excitations
of those fields. These excitations are (usually) localised (the exceptions
are unbound unrenormalised massless particles such as bare photons --
although note that by localised I don't mean that they exist at a single
point as in classical physics but that their amplitude at any given
moment in time is spread over a
small volume),
and thus take on some properties which we associate with particles.
These excitations are the primary object of study in field theory.
Thus we can think of field theory as a study of particles, just not the
same sort of particles that are studied in classical mechanics. This is,
of course, how I usually approach it.

The vacuum in quantum field theory plays an important role. This is defined
as the lowest energy state. One might think that the lowest energy state
is one in which there are no excitations, and thus no particles, and
thus qualifies as nothing. However, this isn't the case. Naively, one
might might question whether the lowest energy state is a zero energy
state. However, in non-gravitational quantum physics, all we measure are
energy differences, so it is not clear that it is possible to uniquely
define an point of absolute zero energy. This might change when we
introduce gravity. But more importantly, there are various structures
in the quantum vacuum that exist in even the lowest energy state.
Carroll lists a few examples. I will add the topological structures in
the gluonic field, such as monopoles, instantons, vortices, and so on.

The gluonic field is the field that drives the strong nuclear force,
and is responsible for holding the nucleus of the atom together (among
other things).

A topological invariant is a quantity which doesn't change
under continuous changes in the vacuum. For example, we might think about
the number of times something encloses something else. Consider a ball
and a balloon (which is fully sealed up). We can either place the ball
inside the balloon, or outside it. We label all the states where the ball
is outside the balloon with the number zero (mathematically, this
number is referred to as the Pontryagin index or winding number).
We label all the states where
the ball is inside the balloon with the number one. This number describes
the number of times the balloon is wrapped around the ball. We can move
the two objects around, deform the shape of the balloon, and by processes
such as this transform from any one winding number zero state to any other
winding number zero state. And equally from any winding number one state
to any other winding number one state. But we can't get from a winding
number zero state to a winding number one state by just moving things
around. We have to burst the balloon to get the ball outside it.

Winding numbers also appear in physical systems. In particular,
the possible states of the gluonic field can be split into different
sub-sets with different winding numbers. These winding numbers are
associated with various structures in the field, or the topological
objects. The point is, once these
structures are present, you can't get rid of them by continuous
transformations. You can move the instantons, vortices and monopoles
around, you can add in additional pairs of structures with winding number
plus and minus one (thus preserving the total winding number), but
ultimately you can't get rid of them. The lowest energy state which can
be reached by a physical process won't be a state where nothing exists.

As Carroll notes, it might be that the most symmetric vacuum (i.e. without
any structures, winding number zero) is not the minimum energy state.
In this case, the system would naturally prefer one of the states
with non-zero winding number. Thus some people people argue, there is
something rather than nothing because nothing is unstable, if we allow us
to be able to define nothing as a symmetric false vacuum state. But this
has nothing to do with the universe, since it does not explain why there
are fields at all in which there can be vacuum states, symmetric or
otherwise.

Carroll also dismisses the relevance of quantum fluctuations (such as an
electron and positron popping out of the vacuum for a short period of time).
This picture is sometimes used, with justification from the uncertainty
principle, interpreted to mean that there can be a small fluctuation of
energy in a short period of time. I have always disagreed with this:
All QFT processes satisfy the conservation of energy and momentum at the
level of creation and annihilation processes. A fluctuation of this type would
violate that. Such
disconnected diagrams don't play any role in a perturbative expansion,
and there is no reason to suppose that they could be non-perturbative effects.
Carroll notes another reason for rejecting this: a true vacuum state (or a true
state of nothing) would be stable, while if these particles could emerge it
would imply an unstable state, and thus not nothing.

Then there are issues from quantum gravity. Firstly, most theories of quantum
gravity treat space and time as a quantum object, which runs against our
classical intuition. The notion of empty space and space filled with stuff
blurs. Instead, space-time itself becomes stuff.

Secondly, there is the issue of whether quantum gravity implies a beginning of the
universe. Classically, an initial singularity is guaranteed, and this is supported
by the overwhelming evidence for inflation and a big bang. However, quantum
effects certainly will make the classical arguments break down, and might
mean that it is possible to avoid the initial singularity. However this is
all still very much uncertain.

The only additional point we need to ask is whether we can say even this
much. I am not convinced that trying to quantise space and time is the best
way of combining general relativity and quantum field theory. I discuss that
possibility in detail in chapter 15 of my book.

But broadly speaking, I agree with Carroll here. Most attempts by physicists
to answer this question have always started with something that isn't nothing.
That isn't acceptable.

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